Orchids need air circulation, so putting them in that kind of atmosphere is no good at all. Some hothouse types will live in large 'greenhouse' environments, especially if all else is provided knowledgably, but otherwise I wouldn't suggest it.

There are a few orchids that like additional humidity but will still need air circulation. Paphiopedalums and Phalaenopsis are two good suggestions. You still do not want to cut all air circulation off and it would be best if you could also incorporate a small fan to help move the air. Another consideration is that sunlight passing through glass can be greatly magnified and burn leaves so choosing species/varieties that need less light would be a better option. Can you hang plants anywhere or will the cats still jump up on them?

Richard

First issue is "how big" are these plants in question? Yes it is possible to grow orchids in an 'orchidarium' [a terr being used for orchids] but most dens & oncs that I have seen would require a REALLY large terr. I do grow some orchids in a terr, but they are all miniatures.

The vase idea amounts to a death sentence. A lot of big box stores display plants in manners/set-ups they find attractive but are detrimental to the lives of the plants themselves.

In a terr, you must ensure that your set-up has good air circulation, as Richard mentioned. PC fans are often used to provide this.

No, your best bet is likely to learn how to grow them outside of a terr. Given that you're in Calif, depending on the climate in you particular area [as I recall, Cal has a LOT of different microclimates], you very well might be able to grow them outdoors.

Most store bought orchids are incorrectly potted -- ie. in a pot that is way too big or in the wrong media/potting mix.

Additionaly, I will add that improper watering [90% of the time being overwatering] is the most common cause of orchid death.

Have you considered finding a local orchid society in your area? [You could probably do a Google search to find local societies -- many have their own websites detailing when and where they meet. You might also try posting in the orchid forum querying as to societies in your area.] The folks at an O.S. would be able to take a gander at your new acquisitions and provide you with information as to their care.